Likelihood for Generally Coarsened Observations from Multistate or Counting Process Models

Daniel Commenges and Anne Gégout‐petit

Scandinavian Journal of Statistics, 2007, vol. 34, issue 2, 432-450

Abstract: Abstract. We consider first the mixed discrete‐continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other events are observed exactly. A heuristic likelihood can be written for such models, at least for Markov models; however, a formal proof is not easy and has not been given yet. We present a general class of possibly non‐Markov multistate models which can be represented naturally as multivariate counting processes. We give a rigorous derivation of the likelihood based on applying Jacod's formula for the full likelihood and taking conditional expectation for the observed likelihood. A local description of the likelihood allows us to extend the result to a more general coarsening observation scheme proposed by Commenges & Gégout‐Petit. The approach is illustrated by considering models for dementia, institutionalization and death.

Date: 2007
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